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Through his first two starts of the season, Shelby Miller looked like he might be a bit overmatched at Triple-A. But on Wednesday, he showed that he is adjusting to the higher level of competition.

MLB.com's No. 5 prospect allowed one run over five innings, earning his first Triple-A win as the Memphis Redbirds trumped the New Orleans Zephyrs, 7-5.

Miller gave up five hits and walked four in the contest as he lowered his ERA from 9.00 to 6.23. He also struck out nine, giving him 19 punchouts in 13 innings this season.

"Compared to my last couple of starts, this was definitely better," Miller said. "I made a couple mistakes, but it happens. I'm excited where I'm at now considering how my last few starts have gone though."

The only run the 21-year-old right-hander gave up came in the fourth, when No. 2 Marlins prospect Matt Dominguez led off the inning with a solo homer. Miller also ran into some trouble in the third, as he surrendered a one-out single to Donovan Solano followed by a walk to Bryan Petersen. Miller then loaded the bases by walking Cole Armstrong with two outs, but got out of the inning by inducing a flyout off the bat of Chris Aguila.

"He wasn't real sharp tonight, but he made pitches when he had to and he put up zeroes," Redbirds manager Ron Warner told the Memphis Commercial Appeal. "He gave up the solo home run and pitched himself out of some jams throughout the game. That's expected from a young kid still learning."

Miller's easiest frame of the day was his last, as he worked his only 1-2-3 inning in the fifth.

"Shelby did a great job," said No. 9 Cardinals prospect Matt Adams. The first baseman also doubled in the win. "Everyone believes we have a good lineup and a great offense so the runs will come, like they did tonight."

Selected 19th overall by the Cardinals in 2009, Miller earned the team's Minor League Pitcher of the Year Award in 2011 for the second straight season. He combined to go 11-6 with a 2.77 ERA in 139 2/3 innings between Class A Advanced and Double-A last year, striking out 170 and walking 53.

The Texas native struggled in his first two starts at Triple-A, however, giving up a combined four runs on 13 hits in eight innings. One of Miller's problems so far has been his susceptibility to the longball. He has surrendered four roundtrippers in his three outings.

The Redbirds' offense was led Wednesday by Amaury Cazana, who went 2-for-4 with a double, three RBIs and a run scored. Miller, who recorded two RBIs in 13 plate appearances last year, also plated a run with a bases-loaded walk in the first.

Skip Schumaker, recovering from a torn right oblique muscle, went 2-for-4 with a run scored out of the leadoff spot for Memphis. He is batting .300 (3-for-9) through the first three games of his rehab assignment.

David Heck is a contributor to MLB.com. This story was not subject to the approval of the National Association of Professional Baseball Leagues or its clubs.